Why is current constant in a series connection? AND fluid flow in pipe

My physics book explains that this is because of the conservation of charge and the fact that charge doesn't accumulate at a certain point.

Can someone please explain this in detail, especially the part where it says that charge can't accumulate.

Another question which i think is similar is the amount of mass flowing into and out of a pipe. My professor used the conservation of mass to show that the mass of fluid flowing into the pipe is equal to the mass flowing out. Isn't it possible that the fluid accumulates inside the pipe and gets compressed, so that the mass flowing out will be less than the mass flowing in?
Thanks!

It is possible for material flowing into a pipe to compress so you, for a while, get less out than you put in. For a while. However, after a while the pressure of the trapped fluid gets high enough that the outflow = inflow once again. (An electrical component which acts like that would be considered "reactive" rather than ohmic - like a capacitor. I take it you are still just looking at DC loads?)

Now go look up compressability of water - it's so small that we usually treat water as uncompressable.

As far as the fluid-flow model for electric circuits is concerned, the "fluid" is always considered to be uncompressable. It's only a model ... a kind of metaphor to help you think about electric circuits. You will always be able to find some places where it doesn't work.

Isn't it possible that the fluid accumulates inside the pipe and gets compressed

You are perfectly right.
Conservation of mass in fluid dynamics usually includes a term that describes the mass stored inside of the system due to compressability or other effects. If this stored mass does not change with the time, then this is a special case called a steady state flow. And only in steady state flow the same amount of fluid is coming out of the pipe as the pipe is fed at the other end. You usually encounter unsteady flow effects on startup / shutdown of gas pipelines or when the flow is decreased / increased which usually needs a modification in the operating pressure.

In electricity startup and shutdown are so very fast, that you would not notice such effects unless you une scope and visualise the first milliseconds after you turned on he light or such. So we usually have a steady state flow here with the same flow (=current) throughout the series connection.

I may be wrong but I also understand this phenomena as being an experimental verifcation of pauli's exclusion principle that no two electrons can be in the same state at the same time and so if electrons leave a wire, there are only positions left to fill those spaces and no more. What goes in must come out, no more no less.

I may be wrong but I also understand this phenomena as being an experimental verifcation of pauli's exclusion principle that no two electrons can be in the same state at the same time and so if electrons leave a wire, there are only positions left to fill those spaces and no more. What goes in must come out, no more no less.

This is not true, at least for conduction in metals. There's no limit to the number of electrons in the conduction band. This is only kept very close to the number of metal ions, because a slight imbalance would produce a large electric field.

A small piece of wire would have a self-capacitance of about 1 pF.
This means that a piece of wire at 1V would have a charge of only 10^-12 Coulomb.
It would have only 6.2 million electrons less than a piece of wire at 0V.

1g = 1/63.5 mole of copper would have 6*10^23 /63.5 = about 10^22 copper atoms, and also about 10^22 electrons in the conducion band, so you only need to remove one electron in 1.6 * 10^15 to raise the potential with 1 volt. To remove in electron in 10^10 you'd need to put 160 kV on it.
This explains why the electron fluid appears nearly incompressible.

Staff: Mentor

So charge builds up on a capacitor... But if too much does, breakdown can allow that plugged up charge to continue.

While it often serves the purpose to speak of a capacitor as "storing charge", it is important to realize that it really does not. And in the context of the topic of this thread, it is doubly important to understand that a capacitor does not store up charge: as many electrons flow into the wire going to one side of the capacitor as simultaneously flow out from the other side into the rest of the series circuit. (*)

No charge gets delayed, waylaid, or squirrelled away and cannot be accounted for; there definitely is no "plugged up" charge anywhere in a series circuit (nor in any circuit, for that matter).

So why do we even say that capacitors store charge? That's a topic for another day....

(*) for this reason, we can speak of current flowing through a capacitor despite knowing there is an insulating layer at the centre of every capacitor